Three sources of error are pointed out: (1) technique of making smears; (2) ability of the observer to classify the various cells; (3) chance variations in distribution (the subject of this paper). The magnitude of this chance error can be estimated by determining the standard deviation [S.D.], since an error due entirely to chance is unlikely to be more than 3 times the S.D. above or below the true value. The S.D. can be calculated according to the formula [sigma]= (pqN)1/2, where [sigma] is the S.D., p is the % of a certain type of cell, q is the % of all other types together, and N is the no. of cells counted. This S.D., calculated for various types of cells, agreed closely with the actual S.D. observed in 100 differential counts of 100 cells each on the same sample of blood. It is pointed out that this chance error is of considerable magnitude, amounting in a count on 100 cells to as much as 15% on either side of the true %. The error can be decreased only by counting a larger no. of cells. Not less than 400 leucocytes should be counted if a reasonably accurate differential count is to be obtained.